# If a number is selected at random from the integers 1 through 12, what is the probability that it is even or divisible by 3?

66 views

closed

If a number is selected at random from the integers 1 through 12, what is the probability that it is even or divisible by 3?

1. 2/3
2. 1/2
3. 1/3
4. 0

by (54.3k points)
selected

Correct Answer - Option 1 : 2/3

Concept:

If S is a sample space and E is a favourable event then the probability of E is given by:

$\rm P(E)=\frac{n(E)}{n(S)}$

Note: OR means Union

Calculation:

The set, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is a sample space for the given experiment.

The numbers that are even or divisible by 3 are 2, 3, 4, 6, 8, 9, 10, 12

So the set E = {2, 3, 4, 6, 8, 9, 10, 12} describes the event.

$\rm P \left( {{\rm\text{Even or divisible by 3}}} \right) = \frac{{n\left( E \right)}}{{n\left( S \right)}} = \frac{8}{{12}} = \frac{2}{3}$